H=-16t^2+5t+52

Solution for H=-16t^2+5t+52 equation:

=-16H^2+5H+52

We move all terms to the left:

-(-16H^2+5H+52)=0

We get rid of parentheses

16H^2-5H-52=0

a = 16; b = -5; c = -52;
Δ = b2-4ac
Δ = -52-4·16·(-52)
Δ = 3353
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{3353}}{2*16}=\frac{5-\sqrt{3353}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{3353}}{2*16}=\frac{5+\sqrt{3353}}{32}
$